X-ray spectral studies of groups have followed the techniques previously
used for other diffuse X-ray sources such as elliptical galaxies and
rich clusters. The observed data from X-ray instruments such as ROSAT or
ASCA do not give the actual spectrum of the source but a convolution of
the source spectrum with the instrument response. In general, it is not
possible to uniquely invert the convolution and obtain the input
spectrum. The usual solution is to adopt a model spectrum with a few
adjustable parameters and to find the best fit to the observed data. By
analogy to rich clusters, it has generally been assumed that the
dominant emission mechanism in groups is thermal emission from diffuse,
low-density gas. Many authors have calculated the spectrum emitted by a
hot, optically thin plasma. The most popular models are that of
Raymond & Smith
(1977)
and Mewe and collaborators (the so-called MEKAL model;
Mewe et al 1985,
Kaastra & Mewe
1993,
Liedahl et al
1995).
For simplicity, single-temperature (i.e. isothermal) models are usually
assumed. The free parameters of interest in the isothermal plasma models
include the gas temperature and metal abundance. For very hot systems,
such as rich clusters, the X-ray emission in the isothermal model is
dominated by the free-free continuum from hydrogen and helium. For the
temperatures more typical of groups (~ 107 K), much of the
flux is found in line emission and bound-free continuum.

3.4.1. Gas Temperature
In general, isothermal plasma models provide good fits to the ROSAT PSPC
spectra of groups. The derived gas temperatures are in the range ~
0.3-1.8 keV (see Figure 3),
which is roughly what is expected given the range of observed velocity
dispersions for groups (e.g.
Ponman et al 1996,
Mulchaey et al
1996a,
Mulchaey &
Zabludoff 1998,
Helsdon & Ponman
2000).
There is generally good agreement in the literature on the temperature
of the gas; multiple authors have derived temperature values within 10%
of each other, even when temperatures were derived over vastly different
physical apertures (e.g.
Mulchaey et al
1996a).
The temperatures derived from the different plasma models
(i.e. Raymond-Smith, MekaL) are also fairly consistent with each other
(e.g.
Mulchaey &
Zabludoff 1998).
Furthermore, there is very good agreement between gas temperatures
determined by the ROSAT PSPC and ASCA for systems with temperatures less
than about 2 keV. For higher-temperature gas (i.e. clusters), the ROSAT
data appear to underestimate the true gas temperature by approximately
30%
(Hwang et al 1999).
All these observations suggest that the derived temperatures for the
intragroup medium are fairly robust.

For some of the groups observed by ROSAT, it is possible to measure
temperature profiles for the hot gas
(Ponman & Bertram
1993,
David et al 1994,
Doe et al 1995,
Davis et al 1996,
Trinchieri et al
1997,
Mulchaey &
Zabludoff 1998,
Helsdon & Ponman
2000,
Buote 2000b).
These profiles suggest that the gas is not strictly isothermal, but
rather follows a somewhat universal form: the gas temperature is at a
minimum at the center of the group, rises to a temperature maximum in
the inner ~ 50-75 h-1100 kpc, and drops gradually
at large radii. The temperature minimum in the inner regions of the
group is coincident with the sharp rise in the X-ray surface brightness
profile. This behavior is consistent with that expected from a "cooling
flow" (cf
Fabian 1994).
The temperature drop at larger radii is often based on lower-quality
spectra, and in most cases is not statistically significant. Even if
this latter effect is present, the gas temperature at large radii is
usually within 10-15% of the temperature maximum. Therefore,
isothermality is not a bad assumption over most of the group, as long as
the central regions are excluded. However, when global gas temperatures
are quoted for groups in the literature, the central regions are almost
always included. Because the central regions dominate the total counts
in the spectrum, the temperatures found in the literature may
underestimate the global temperatures in many cases.

3.4.2.
spec
Although most authors have estimated the ratio of specific energy of the
galaxies to the specific energy of the gas (i.e. the
parameter)
from surface brightness profiles (see
Section 3.3.3),
can in
principle be determined by directly measuring
and
Tgas. Unfortunately, because
is usually derived from
only a few velocity measurements, this method is often not very
robust. Detailed membership studies have been made for a few X-ray
groups (i.e.
Ledlow et al 1996,
Zabludoff &
Mulchaey 1998,
Mahdavi et al
1999),
and in these cases the velocity dispersion estimates are more
reliable. Using such estimates,
Mulchaey &
Zabludoff (1998) found
spec
~ 1 for most of the groups in their sample.
Helsdon & Ponman
(2000)
found a similarly high value for
spec
for groups with temperatures of ~ 1 keV, but noted a trend for
spec to decrease in the lower-temperature
systems. However, almost all of the low-temperture groups in the
Helsdon & Ponman
(2000)
sample have velocity dispersions determined from a small number of
galaxies. Thus, while the current data suggest a trend for
spec
to decrease as the temperature of the group decreases, detailed
spectroscopy of cool groups will be required to verify this result.

The ~ 1
values derived for hot groups from the direct measurement of temperature
and velocity dispersion
(spec) are significantly higher than the values
of often
derived from surface brightness profile fits
(fit). This so-called
-discrepancy
problem has been discussed extensively for rich clusters (e.g.
Mushotzky 1984,
Sarazin 1986,
Edge & Stewart
1991,
Bahcall & Lubin
1994).
Based on simulations,
Navarro et al
(1995)
concluded that
fit
is biased low in galaxy clusters because of the limited radial range
used in the X-ray profiles. This explanation may also explain the
discrepancy found for groups, which are typically detected to a much
smaller fraction of the virial radius than their rich cluster
counterparts. Therefore, the
-discrepancy
in groups may be an indication that the current derived
fit
values underestimate the true
values in
many cases.

3.4.3. Gas Metallicity In
addition to measuring gas temperatures, ROSAT PSPC and ASCA observations
of groups have been used to estimate the metal content of the intragroup
medium. As noted earlier, X-ray spectra of groups are dominated by
emission line features. The strongest emission lines are produced when
an electron in a highly ionized atom is collisionally excited to a
higher level and then radiatively decays to a lower level. The most
important features in the X-ray spectra of groups include the K-shell (n
= 1) transitions of carbon through sulfur and the L-shell (n = 2)
transitions of silicon through iron. Particularly important is the Fe
L-shell complex in the spectral range ~ 0.7-2.0 keV
(Liedahl et al
1995).
The wealth of line features in the soft X-ray band potentially provides
powerful diagnostics of the physical conditions of the gas, including
the excitation mechanism and the elemental abundance
(Mewe 1991,
Liedahl et al 1990).

Several potential problems have been noted with the low metallicity
measurements for the intragroup medium.
Ishimaru & Arimoto
(1997)
pointed out that most X-ray studies have adopted the old photospheric
value for the solar Fe abundance (Fe/H ~ 4.68 × 10-5),
whereas the commonly accepted "meteoritic" value is significantly lower
(Fe/H ~ 3.24 × 10-5). (Note that more recent estimates
of the photospheric Fe abundance in the sun are consistent with the
meteoritic value; see
McWilliam 1997.)
Thus, essentially all the Fe measurements in the X-ray literature should
be increased by a factor of ~ 1.44 to renormalize to the meteoritic
value. This is particularly important when comparing the X-ray
metallicities to chemical-evolution models, which usually adopt the
meteoritic Fe solar abundance. The ability of ROSAT data to properly
measure the gas abundance has also been questioned.
Bauer & Bregman
(1996)
measured metallicities with the ROSAT PSPC for stars with known
metallicities close to the solar value, and found the ROSAT
metallicities were typically a factor of five lower than the optical
measurements.
Bauer & Bregman
(1996)
suggested several possible explanations for the discrepancy, including
instrumental calibration uncertainties, problems with the plasma codes
and possible differences in the photospheric and coronal abundances of
stars. Instrumental uncertainties with the ROSAT PSPC are unlikely to be
the major source of the problem because ASCA spectroscopy of groups also
indicates low gas metallicities
(Fukazawa et al
1996,
1998,
Davis et al 1999,
Finoguenov & Ponman
1999,
Hwang et al 1999).
The possibility that the plasma models are inaccurate or incomplete has
been a major concern. While abundance measurements for rich clusters are
derived primarily from the well-understood Fe
K- line, group
measurements rely on the much more complicated Fe L-shell
physics. Problems with the plasma models were in fact identified by
early ASCA observations of cooling flow clusters
(Fabian et al 1994).
Liedahl et al's
(1995)
revision to the standard MEKA thermal emission model likely accounts for
the largest problems in the earlier plasma codes. However, fits to ASCA
spectra of groups with the revised model still require very low metal
abundances.
Hwang et al (1997)
have shown that for clusters with sufficient Fe L and Fe K emission
(i.e. clusters with temperatures in the range ~ 2-4 keV), the
metallicities derived from the Fe L line complex are consistent with the
values derived from the better understood Fe K complex (see also
Arimoto et al's 1997
analysis of the Virgo cluster). Unfortunately, it is not clear that the
reliability of the Fe L diagnostics implied from ~ 2-4 keV poor clusters
necessarily extends down to lower temperature groups, since other Fe
lines dominate the spectrum below ~ 1 keV
(Arimoto et al 1997).
Therefore, some problems with the plasma models may still exist.

Another potentially important problem is that the usually assumed
isothermal model may be inappropriate for groups
(Trinchieri et al
1997,
Buote 1999,
2000a).
There is clear evidence for temperature gradients in groups,
particularly in the inner ~ 50 h-1100 kpc. In
fact, the surface brightness profiles of ROSAT PSPC data suggest the
presence of at least two distinct components in groups
(Mulchaey &
Zabludoff 1998).
Mixing of multiple-temperature components is particularly an issue for
ASCA data because separating out the central component from more
extended emission is not possible with the ASCA point spread function.
Buote (1999,
2000a)
has studied this problem in detail for both elliptical galaxies and
groups, and finds that in general single-temperature models provide poor
fits to the ASCA spectra. By adopting a two-temperature model, one can
obtain better fits, and the metallicities derived are substantially
higher. For a sample of 12 groups,
Buote (2000a)
derives an average metallicity of Z = 0.29 ± 0.12
Z for the
isothermal model and Z = 0.75 ± 0.24
Z for the
two-temperature model (a single metallicity is assumed for the gas in
these models).
Buote (2000a)
also finds that a multiphase cooling flow model provides a good
description of the data. This model also requires higher metallicities
(Z = 0.65 ± 0.17
Z).
Buote (2000a)
finds a trend for the metallicities to be lowest in those groups for
which the largest extraction apertures were used. This result is
consistent with metallicity gradients in groups (see also
Buote 2000c).
Alternatively, it may simply reflect that the relative contribution of
the "group" gas component increases as one adopts a larger aperture. In
fact, given the results of the ROSAT surface brightness profile fits,
emission from the central elliptical galaxy may dominate the flux in the
typical ASCA aperture and thus likely dominates the metallicity
measurement. Therefore, the ASCA measurements may not be providing an
accurate gauge of the global metal content of the group gas. Regardless,
the work of
Buote (1999,
2000a)
is an important reminder that the properties derived from X-ray
spectroscopy are very sensitive to the choice of the input model.

Matsushita et al
(2000)
also considered multi-temperature models for a large sample of
early-type galaxies observed with ASCA. In contrast to
Buote (1999,
2000a),
Matsushita et al
(2000)
concluded that the poor spectral fits to ASCA data were not caused by
incorrect modeling of multi-temperature emission. Furthermore, the
multi-temperature models used by
Matsushita et al
(2000)
produced relatively small increases in the overall abundance in many
cases.
Matsushita et al
(2000)
suggested that the strong coupling between the abundance of the
so-called -elements
(i.e. O, Ne, Mg, Si, S) and the abundance of Fe hampers a unique
determination of the overall metallicity. By fixing the abundance of the
-elements,
Matsushita et al
(2000)
found that the derived metallicities are approximately solar. Although
Matsushita et al
(2000)
restricted their analysis to early-type galaxies, these results may be
applicable to groups, which have X-ray properties very similar to those
of X-ray luminous ellipticals.

Although the dominant line features for the intragroup medium are
produced by iron, strong lines are also expected from elements such as
oxygen, neon, magnesium, silicon, and sulfur. The relative abundance of
these various elements provides strong constraints on the star formation
history of the gas. Some authors have attempted to fit the ASCA spectra
with an isothermal model where the
-elements are varied
together and separately from the iron abundance
(Fukazawa et al
1996,
1998;
Davis et al 1999;
Finoguenov & Ponman
1999;
Hwang et al 1999).
In general, these studies find that the
-element to iron ratio
is approximately solar in groups. Unfortunately, the determination of
this ratio is very sensitive to the spectral model adopted
(Buote 2000a)
and if the isothermal assumption is not valid, these determinations are
not particularly meaningful.

In summary, despite the great potential of X-ray spectroscopy to provide
clues into the enrichment history of the intragroup medium, it is not
possible at the present time to make strong conclusions about the metal
content of the hot gas. Until we have higher resolution X-ray spectra
and more complete plasma codes, the metallicity of the intragroup medium
will remain an open issue.

3.4.4. Absorbing Column
The soft X-ray band is sensitive to low-energy photoabsorption by gas
both within the source and along the line of sight. This absorption must
be included in the X-ray spectral fits. It is usually assumed that the
X-ray flux is diminished by:

where NH is the hydrogen column density and
(E) is the
photo-electric cross section (solar abundances are almost universally
assumed for the absorbing gas). The cross sections in
Morrison & McCammon
(1983)
are commonly adopted for X-ray analysis. The standard procedure is to
allow NH to be a free parameter in the spectral fit. If the
best-fit spectral model returns a value of NH significantly
higher than the Galactic value, this is taken as evidence for excess
absorption intrinsic to the group or central galaxy. The ROSAT and ASCA
spectra of groups are often not of high enough quality to adequately
constrain the absorbing column. Therefore, many authors have chosen to
fix NH to the Galactic value for spectral fits. For a few
groups, however, column densities above the Galactic value have been
inferred
(Fukazawa et al
1996;
Davis et al 1999;
Buote 2000a,
b).
Buote (2000b)
undertook the most ambitious study of absorption in groups, measuring
NH as a function of radius in a sample of 10 luminous systems
observed by the ROSAT PSPC.
Buote (2000b)
found that the value of NH derived depends strongly on the
bandpass used in the X-ray analysis and suggested the bandpass-dependent
NH values are consistent with additional absorption in the
group from a collisionally ionized gas. This excess absorption manifests
itself primarily as a strong oxygen edge feature at ~ 0.5 keV.
Buote (2000b)
found that within the central regions of the groups, the estimated
masses of the absorbers are consistent with the matter deposited by a
cooling flow over the lifetime of the flow. If a warm absorber exists in
groups, as suggested by
Buote (2000b),
it should be verified by the next generation of X-ray telescopes.

3.4.5. X-Ray Luminosity
For a thermal plasma, the X-ray luminosity is a rough measure of the
total mass in gas. Therefore, the total X-ray luminosity of a group
provides a potentially interesting probe of a group's properties. In
almost all cases in the literature, the total flux or luminosity quoted
is out to the radius to which X-ray emission is detected. In this sense,
quoted X-ray luminosities should be thought of as "isophotal
luminosities." The measured luminosity is also sensitive to the exact
techniques used in the X-ray analysis. For example, the total radial
extent of the X-ray emission (and thus the total X-ray luminosity) is
strongly dependent on the assumed background level
(Henriksen & Mamon
1994,
Davis et al 1996).
Because of this, different authors often derive vastly different X-ray
luminosities for the same group using the same ROSAT observation
(Mulchaey et al 1996a).

It is a common practice to quote bolometric luminosities in the
literature. The bolometric correction is estimated by extrapolating the
spectral model for the gas beyond the limited bandpass of the particular
telescope and by making a correction for any absorption along the line
of sight. In the case of ROSAT observations, these corrections can
easily double the luminosity of the source. The bolometric correction is
also somewhat sensitive to uncertainties in the spectral model such as
gas metallicity. For very shallow observations, such as those based on
ROSAT All-Sky Survey data, a spectral model must usually be assumed to
estimate the total X-ray luminosity. The bolometric luminosities of
groups are typically in the range several times 1040
h-2100 to nearly 1043
h-2100
(Mulchaey et al
1996a,
Ponman et al 1996,
Helsdon & Ponman
2000).
Thus, the X-ray luminosities of groups can be several orders of
magnitude lower than the X-ray luminosities of rich clusters (cf
Forman & Jones
1982).

Finally, it is worth noting that because X-ray emission is usually
traced only to a fraction of the virial radius in groups, it is likely
that the isophotal measurements significantly underestimate the true
luminosities of the hot gas. This is particularly true for the coolest
groups.
Helsdon & Ponman
(2000)
have attempted to account for the missing luminosity by extrapolating
the gas density profile models out to the virial radius. A comparison of
the observed isophotal luminosities to the corrected virial luminosities
in the Helsdon & Ponman sample indicate that in many cases, over
half of the luminosity could occur beyond the radius to which X-ray
emission is currently detected.